bought the '99 AWD RX300 in 2003. had some issues, but the extended warranty took care of it up to 100k. no transmission issues so far (~125k miles).
the car is great, and as long as you properly maintain it (oil changes every 4-5k miles as Nelli mentioned), then the car will take good care of you. I'm hoping that car will give me another 5-6 years or 100k miles.
the only downside to this car is lack of in-dash nav and AUX unput. however, mounting a GPS to the windshield is not too difficult and someone on here showed how to install a AUX input.
no issues with the key (just make sure that the battery is fresh).
oh, one other item - make sure that the heated seats work. these tend to burn out around 100k, and replacing a new one is about $1k. so when testing the heated seats, make sure that the bottom heats as well as the back. if the bottom gets too hot too quickly, then that means it is going to burn out real soon.
hope this helps....